The cosecant of ∠G is 1/sin(∠G) = 37/35
The cosecant of an angle is defined as the reciprocal of the sine of the angle. To find the sine of ∠G, we can use the Pythagorean theorem on the right triangle GHI:
The Pythagorean theorem is a mathematical principle that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, [tex]H^2 = side^2 + side^2[/tex]
[tex]35^2 + 12^2 = GI^2 + IH^2 = HG^2[/tex]
1225 + 144 = 1225 + 144 = [tex]37^2[/tex]
1369 = 1369 = 1369
So, HG = 37.
Hence, the sine of ∠G is 35/37.
Therefore, the cosecant of ∠G is 1/sin(∠G) = 37/35.
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The variable whose effect on the response variable is to be assessed by the experimenter.
In an experiment, the variable being measured or tested is known as the dependent variable.
What is dependent variable?Any variable whose value depends on an independent variable is said to be dependent. The thing being measured in an experiment or assessed in a mathematical equation is the dependent variable. Sometimes the dependent variable is referred to as "the result variable." A dependent variable is one that depends on the value of another variable in an expression. As an illustration, if y = 2x, then y relies on x Consequently, y Equals 2 if x = 1. The independent variable is the one whose value is unrelated to the other variables. The dependent variable is the one whose value depends on the independent variable. When the same line is written in two different ways so that there are infinite solutions, an equation system is referred to as dependent.To learn more about dependent variable, refer to:
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Cone A and cone B are mathematically similar. The ratio of the surface area of cone A to the surface area of cone B is 25:4 The volume of cone A is 6000 cm³ Work out the volume of cone B. Optional working
The volume of cone B is calculated as: 384 cm³.
How to Find the Volume of Similar Cones?If the ratio of the surface area of cone A to the surface area of cone B is 25:4, then the ratio of the radii of the cones is 5:2 (since the surface area of a cone is proportional to the square of the radius).
Since the cones are similar, the ratio of their volumes is also the ratio of the cubes of their radii, which is 125:8.
So, if the volume of cone A is 6000 cm³, then the volume of cone B is (6000 * 8) / 125 = 384 cm³.
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also this one would help me out alot
The line that connects the coordinates (7,5) and (9,5) has the equation y = 5.
What is coordinates?A point or shape's location in a two-dimensional plane can be found using coordinates, which are a pair of numbers. The terms "x-coordinate" and "y-coordinate" are used to define a point's location on a 2D plane. A group of values that exhibit precise positioning On graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up. In order to determine a point's coordinates in a coordinate system, you must do the opposite.Due to the fact that the slope of the line across the two points (x1, y1) and (x2, y2) [tex]$\mathrm{m}=\frac{\mathrm{y}_2-\mathrm{y}_1}{\mathrm{x}_2-\mathrm{x}_1}$[/tex] Now, as shown below, we can determine the slope of the line through points (7,5) and (-9,5):
[tex]$\mathrm{m}=\frac{5-5}{-9-7}=\frac{0}{-16}=0[/tex]
As a result, the line's slope is o.
Find the y-intercept now by using the slope and one of the two points.
y = mx + b
5 = (0)(7) + b
b = 5
Equation in slope intercept form is written as follows:
y = mx + b
y = (0)x + 5
y = 5
Consequently, y = 5 is the line's equation.
The complete question is:
Find the equation of the line that passes through the points (7,5) and (−9,5)
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The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined. The slope of the line for coordinates (2, 3) and (2, -3) is undefined.
What is slope of the line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Given that,
The coordinates of two points are:
(x1, y1) = (-7, 5) and
(x2, y2) = (-7, 9).
The slope of the line is given by the following equation:
m = (y2 - y1) / (x2 - x1)
Substituting the value of the given coordinates we have:
m = (9 - 5) / (-7 - (-7))
m = (4)/ -7 + 7 = undefined
The slope of the line given by the coordinates of two points (x1, y1) = (-7, 5) and (x2, y2) = (-7, 9) is undefined.
Similarly, for the coordinates (2, 3) and (2, -3):
m = (y2 - y1) / (x2 - x1)
m = (-3 -3) / (2 - 2)
m = undefined.
Hence, the slope of the line for coordinates (2, 3) and (2, -3) is undefined.
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clay made 4/5 of a pound of a trait mix if he puts 2/5 of a pound into each bag how many bags can clay fill
Answer: 2 bags
Step-by-step explanation:
To determine the number of bags Clay can fill, we need to divide the total amount of the trail mix by the amount of trail mix in each bag.
First, we'll convert the amounts to a common denominator of fifths:
4/5 of a pound of trail mix is 4/5 * 5/5 = 4 fifths
2/5 of a pound is 2/5 * 5/5 = 2 fifths
Now, we can divide the total amount of trail mix by the amount in each bag:
4 fifths ÷ 2 fifths/bag = 2 bags
So, Clay can fill 2 bags with 2/5 of a pound of trail mix each.
please convert the following decimal numbers to binary numbers: (to receive full credit, you must show how you reach your answers. 1 point each, total 5 points): 1) 13 2) 121 3) 252 4) 1023 5) 2049
Answer:
1101 1111001111111001111111111100000000001Step-by-step explanation:
2/13=6 reminder 1
2/6= 3 reminder 0
2/3= 1 reminder 1
2/1= 0 reminder 1
13 becomes 1101 base two/ binary form
The conversion of number from decimal to binary:
[tex](13)_{10}=(1101)_{2}[/tex]
[tex](121)_{10}=(1111001)_{2}[/tex]
[tex](252)_{10}=(11111100)_{2}[/tex]
[tex](1023)_{10}=(1111111111)_{2}[/tex]
[tex](2049)_{10}=(100000000001)_{2}[/tex]
Recursively multiplying the given decimal number by two is one way to convert a decimal number to a binary number. The remainders are then recorded until we arrive at 0 as the final quotient. The remainders are then entered in reverse order to obtain the binary equivalent of the provided decimal number.
The number is 13.
13 ÷ 2 = 6, Remainder = 1
6 ÷ 2 = 3, Remainder = 0
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](13)_{10}=(1101)_{2}[/tex]
The number is 121.
121 ÷ 2 = 60, Remainder = 1
60 ÷ 2 = 30, Remainder = 0
30 ÷ 2 = 15, Remainder = 0
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](121)_{10}=(1111001)_{2}[/tex]
The number is 252.
252 ÷ 2 = 126, Remainder = 0
126 ÷ 2 = 63, Remainder = 0
63 ÷ 2 = 31, Remainder = 1
31 ÷ 2 = 15, Remainder = 1
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](252)_{10}=(11111100)_{2}[/tex]
The number is 1023.
1023 ÷ 2 = 511, Remainder = 1
511 ÷ 2 = 255, Remainder = 1
255 ÷ 2 = 127, Remainder = 1
127 ÷ 2 = 63, Remainder = 1
63 ÷ 2 = 31, Remainder = 1
31 ÷ 2 = 15, Remainder = 1
15 ÷ 2 = 7, Remainder = 1
7 ÷ 2 = 3, Remainder = 1
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, [tex](1023)_{10}=(1111111111)_{2}[/tex]
The number is 2049.
2049 ÷ 2 = 1024, Remainder = 1
1024 ÷ 2 = 512, Remainder = 0
512 ÷ 2 = 256, Remainder = 0
256 ÷ 2 = 128, Remainder = 0
128 ÷ 2 = 64, Remainder = 0
64 ÷ 2 = 32, Remainder = 0
32 ÷ 2 = 16, Remainder = 0
16 ÷ 2 = 8, Remainder = 0
8 ÷ 2 = 4, Remainder = 0
4 ÷ 2 = 2, Remainder = 0
2 ÷ 2 = 1, Remainder = 0
1 ÷ 2 = 0, Remainder = 1
So, [tex](2049)_{10}=(100000000001)_{2}[/tex]
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How to convert psi to atm (atmospheric pressure)?
Take the PSI value and divide it by 14.696 or 14.7 to convert PSI to atm.
What is atmospheric pressure?
The force per unit area that an atmospheric column exerts is known as atmospheric pressure, also known as barometric pressure (that is, the entire body of air above the specified area). A mercury barometer (hence the commonly used synonym barometric pressure) can be used to measure atmospheric pressure because it displays the height of a mercury column that precisely balances the weight of the atmosphere over the barometer. An aneroid barometer, which uses one or more hollow, partially evacuated, corrugated metal discs supported against collapse by an inside or outside spring, can also be used to measure atmospheric pressure. The change in the disk's shape with changing atmospheric pressure can be recorded using a pen arm and a clock-driven revolving drum.
The Imperial system of measurement measures pressures in pounds per square inch (PSI). PSI is frequently used to calculate the pressure of liquids or gases (hydraulic pressure).
The model equation is ATM = PSI/14.7
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When X has the pdf: f(x) = λe^{-λx}λe^(-λx)λe^-λx for x>0
P(X>x) =
A. 1-λe^{-λx}λe^(-λx)λe^-λx
B. 1-λe^{-λx}λe^(-λx)e^-λx
C. λe^{-λx}λe^(-λx)λe^-λx
D. λe^{-λx}λe^(-λx)e^-λx
The probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex]. Thus, option (A) is correct.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain.
P(X>x) is the probability that X takes on a value greater than x, which means that X is in the tail of the distribution. The cumulative distribution function (CDF) of X, denoted F(x), is defined as F(x) = P(X ≤ x). Since the CDF is a cumulative probability, we can find P(X>x) by subtracting the cumulative probability of X being less than or equal to x from 1:
P(X > x) = 1 - P(X ≤ x) = 1 - F(x)
Now, to find F(x), we can use the cumulative density function (pdf) of X. The pdf of X is given by f(x) = λ [tex]e^{- \lambda x}[/tex] for x > 0. To find the cumulative probability, we need to find the definite integral of the pdf from 0 to x:
F(x) = [tex]\int_0^x \lambda e^{- \lambda x}dx[/tex]
= [tex]-e^{-\lambda x} \int_0^x \lambda de^{\lambda x}[/tex]
= [tex]-e^{-\lambda x}[e^{\lambda x}]_0^x[/tex]
= [tex]-e^{-\lambda x}(e^{\lambda x} - 1)[/tex]
= [tex]1 - e^{-\lambda x}[/tex]
Therefore, the probability that X is greater than x is:
P(X>x) = 1 - F(x) = 1 - (1 - [tex]e^{- \lambda x}[/tex] = [tex]e^{- \lambda x}[/tex]
Hence, the probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex].
Option (A) is correct.
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An archer is able to hit the bull's-eye 49% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
a. 0.1267
b. 0.2130
c. 0.7870
d. 0.0010
e. 0.0576
Probability of hitting bull's eye exactly 4 time sin 10 arrows is 0.213
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Properties of Probability:
Phi or a null set is the probability of an impossibly unlikely event.Its sample space represents an event's highest probable probability.Any occurrence has a probability between 0 and 1. A probability can also be zero (0).An event's probability cannot be negative.The chance of A or B happening is equal to the probability of A plus the probability of B if A and B are two outcomes that cannot both occur simultaneously.The probability of hitting a bull's Eye is 49% = 49/100 = 0.49
The probability of not hitting a bull's Eye is = 1- 0.49 = 0.51
Probability of hitting bull's Eye 4 times = (0.49)⁴
Probability of not hitting Bull's eye 6 times = (0.51)⁶
The total number of combinations possible with 10 sets are ¹⁰C₄.
Probability of hitting bull's eye 4 time sin 10 arrows is
¹⁰C₄*(0.49)⁴*(0.51)⁶ = 0.213
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a data analyst creates a scatterplot with a lot of data points. it is difficult for the analyst to distinguish the individual points on the plot because they overlap. what function could the analyst use to make the points easier to find? 1 point geom line() geom jitter() geom point() geom bar()
The analyst could use the geom_jitter() function to make the points easier to find.
What is data analyst ?
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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The analyst could use the geom_jitter() function to make the points easier to find.
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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the picture. please answer it
Answer:5 pounds, and x+y pounds.
Step-by-step explanation:
3 pounds + 2 pounds would equal 5 pounds ,and x pounds plus y pounds are veriables, and we do not have information on how to solve for them, so the answer would just be x pounds plus y pounds.
Step-by-step explanation:
1. If Jaxson buys 2 pounds of kiwi and 3 pounds of raspberries, he buys a total of 2 + 3 = 5 pounds of fruit.
2.If he buys a pounds of kiwi and 7 pounds of raspberries, he buys a total of a + 7 = a + 7 pounds of fruit.
What is x + y + z if [tex]\frac{x}{4-x} = \frac{y}{5-y} = \frac{z}{6-z} = 2[/tex]
A. 8
B. 10
C. 16
D. 6
Step-by-step explanation:
DISCUSSION QUESTIONS (DQ's).
1. Is division always a negative in a religious faith? Why or why not?
For each of the examples below, identify the bearing of D from C.
a)
250°
N
110°
D
b)
145°
D
N
C
215°
Not drawn accurately
a) The bearing of D from C is 250.
b) The bearing of D from C is 145.
What is Bearing in Angle?Angles are measured in bearings clockwise from north. The direction of north must be identified before taking a bearing measurement. The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion.
Given:
a) 250°N, 110°D
As, we know that Bearings are angles, measured clockwise from north. To measure a bearing, we must first know which direction is north.
So, the bearing of D from C is 250.
b) The bearing of D from C in second case is 145.
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Work out the area of a rectangle with base,
b
= 14mm and height,
h
= 10mm.
Answer:
70mm
Step-by-step explanation:
(14*10)/2=70
Height and Width multiplied against each other divided by two is the area of a triangle
You drive your Car for 3 hours at an average speed of 130km per hour. How far did you go?
That's my math question I need help on. Thx!!!
This is quite simple. You just need to multiply. 130 × 3 = 390
Therefore, you would have driven 390 km.
Shortly after takeoff, an airplane is climbing 250 feet for every 1000 feet it travels. Estimate the airplanes climb angle while this is happening.
Answer: The estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°
Step-by-step explanation:
The climb angle of an airplane can be estimated using the tangent of the rise over the run. To do this, you need to know the rise (the vertical distance the airplane is climbing) and the run (the horizontal distance the airplane is traveling).
In this case, the rise is 250 feet and the run is 1000 feet. The tangent of the angle is the rise divided by the run:
tan(angle) = rise / run = 250 / 1000 = 0.25
To find the angle in degrees, you need to take the inverse tangent (arctan) of 0.25:
angle = arctan(0.25) = 14.0°
So, the estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°.
i need help with thus..
Answer: -35/18
Step-by-step explanation: Hello!
The main thing that you need to know when dividing fractions is what the reciprocal is. Here is an example of finding the reciprocal:
1/2 divided by 2/3 = 1/2 x 3/2.
Basically, you flip the second fraction upside down (Put the number under the fraction line over the fraction line and put the number above the fraction line under the fraction line). Then, you multiply the two fractions. Then, you will find the answer. Here is how to do that with the problem you have:
5/3 divided by (-6/7) = ?
After finding the reciprocal, you would get:
5/3 x (-7/6)
To find the answer, multiply the numerators together (5 and -7) and the denominators (3 and 6) together.
For the new numerator, you get -35. For the new denominator, you get 18. Put the new numerator above the fraction line and the new denominator below the fraction line.
The answer is:
-35/18
Why do fractions need to have a common denominator before you add or subtract them? Tell me in the comments below
Explanation: Fractions must have a common denominator to add or subtract because if you think of pieces of a pizza, if you split one pizza into quarters and one into fifths, then each piece won't be the same size, so 1/5 isn't equivalent to 1/4. Therefore, if you subtract or add fractions you need to find a common denominator. One easy way to find a common denominator is list out the multiples of the two (or more) denominators and find the LCM (Least common multiple). Then find the quotient of the LCM divided by the denominator, and multiply that number by the numerator, and you have successfully changed your fraction to an equivalent fraction with a different denominator. Hope this helped. Please vote me brainliest.
How do we solve this’!???
Answer:
n=32 That's all and the stepss
sum of independent negative binomial random variable and geometric random variable
The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.
What is binomial random variable ?
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success or failure.
Let X be a negative binomial random variable with parameters r and p, and let Y be a geometric random variable with parameter q. The sum Z = X + Y is also a random variable.
The cumulative distribution function (CDF) of Z is given by:
F_Z(z) = P(Z <= z) = P(X + Y <= z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)
This expression is a double sum and does not have a closed-form solution, but it can be computed numerically.
Alternatively, the probability mass function (PMF) of Z can be found by counting the number of ways that X and Y can take on their respective values, and summing up their joint probabilities:
f_Z(z) = P(Z = z) = ∑_{x=0}^{z} P(X = x) * P(Y = z - x)
The sum of independent negative binomial and geometric random variables does not have a closed-form distribution and must be computed numerically.
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Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Answer: 90%
Step-by-step explanation: To find the probability of not choosing a red marble, we need to calculate the total number of marbles in the bag and subtract the number of red marbles. The total number of marbles is 3 red + 3 green + 15 yellow + 9 purple = 30. So, the probability of not choosing a red marble is P(not red) = (30 - 3) / 30 = 27 / 30 = 9 / 10=90/100=90%
A bicycle store costs $4000 per month to operate. The store pays an average of $50 per bike. The average selling price of each bicycle is $150. How many bicycles must the store sell each month to break even
Answer:27
Step-by-step explanation:
Answer:
The store would need to sell 40 bikes to break even.
Step-by-step explanation:
In order to break even the store needs to make $4000 a month. They spend $50 per bike and sell them for $150, an easy equation to get their profit per bike is to subtract how .uch they pay for a bike from how much they make per bike which is $150-50=$100. So now we just need to divide $4000 by $100 to find out how many bikes they need to sell. $4000÷$100=40.
for the same frame, complete the free-body diagram of the system abc by adding the forces that act on it.
The total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).
The force of gravity (Fg) acts on the system in the downward direction. This force is equal to the mass of the body multiplied by the acceleration due to gravity (Fg = mg).
The normal force (FN) is the force that acts perpendicular to the surface on which the body is resting. This force is equal to the weight of the body multiplied by the coefficient of friction between the body and the surface (FN = m * g * μ).
The force of friction (Ff) is the force that acts in the opposite direction of the motion of the body. This force is equal to the coefficient of friction multiplied by the normal force (Ff = μ * FN).
The tension force (T) is the force exerted by a string or a cable on the body. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (T = m * a).
The applied force (Fapp) is the force that is applied to the body by an external force. This force is equal to the mass of the body multiplied by the acceleration due to the applied force (Fapp = m * a).
By combining all of these forces, we can determine the total force acting on the system ABC. The total force is equal to the sum of the force of gravity, normal force, friction force, tension force and applied force (Ftotal = Fg + FN + Ff + T + Fapp).
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Complete question:
What is the free-body diagram of the system ABC?
The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l
The surface area of a cone is given by the formula:
S = πl + πr^2
Solving for l, we can start by isolating l on one side of the equation:
S - πr^2 = πl
Dividing both sides by π:
(S - πr^2) / π = l
Therefore, the length l can be found by subtracting the product of π and r^2 from the surface area S, and dividing the result by π.
Profeor Smart i teaching her tudent how the formula for the area of a circle wa derived
The area of circle can be calculated by using the formulas: Area = π x r2, in terms of radius 'r'. Area = (π/4) x d2,
State area of circle?
The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.Area = length x breadthArea = l × b. Area = π × radius × radiusArea = π × r2(π = 3.14) Using these formulas, area for different quadrilaterals (a special case of polygons with four sides and angles ≠ 90o) is also calculated. Application.We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.To learn more about circle refers to:
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Claudia is walking at a constant speed in front of a motion sensor. After 1 s she is 2. 5 m from the sensor. 2s later and she is 4. 0 m from the sensor. Find the equation in the form d=mt+b that describes her motion
The distance is 5.5 meters from the sensor.
Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
Let us assume that d means distance and t means time.
When t = 1, d = 2.5
When t = 3, d = 4
d = mt + b
2.5 = m + b [t = 1]
4.0 = 3m + b [t = 2]
1.5 = 2m [subtract]
m = .75 = slope
b = 1.75 = d-intercept
d = .75t + 1.75
d = 15/4 + 7/4 [t = 5]
d = 22/4 = 5.5 m from sensor
Thus, the distance is 5.5 meters from the sensor.
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The table shows how much a frozen yogurt shop
charges for its yogurt. Write an expression to show
how much it costs to buy a small yogurt with no
toppings and a large yogurt with x toppings. Then
solve for buying a small yogurt with no toppings
and a large yogurt with 3 toppings.
The expression for the cost is cost = 0.35x + 7.5 and the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings is $8.55
To write an expression to show how much it costs to buy a small yogurt with no toppings,
The expression for the costs of a small yogurt with no toppings and a large yogurt with x toppings will be:
Cost = 2.85 + (4.65 + 0.35x)
Cost = 2.85 + 4.65 + 0.35x
Cost = 0.35x + 7.5
To find the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings, substitute x = 3 into the above expression. That is:
Cost = 0.35x + 7.5
Cost = 0.35(3) + 7.5
Cost = $8.55
Thus, the total cost is $8.55
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Find the equation of the line passing through (-8,3) and (-6, 7). Write your equation in point-slope AND slope-intercept forms. Use the first point in your point-slope form!
point-slope form:
slope-intercept form:
Answer:
point-slope form: y - 3 = 2(x+8)
slope-int form: y = 2x + 19
Step-by-step explanation:
For slope-int form, find the slope of the line.
7-3 / -6-(-8) = 4/2 = 2
This becomes y = 2x + b
To find b: plug in a y-coordinate for the y in the equation and plug in an x-coordinate for the x
7 = 2(-6) + b
7 = -24/2 + b
7 = -12 + b
7 + 12 = -12 + 12 +b
19 = b
The final equation is: y = 2x + 19
Need help please on this
The line has an equation y = 0.03x + 20, with a slope of $0.03 per GB and the y intercept of $20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let y represent the total cost of buying x gigabyte of data
The line passes through the point (0, 20) and (2000, 80). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-20=\frac{80-20}{2000-0} (x-0)\\\\y = 0.03x + 20[/tex]
The slope is 0.03 and the y intercept of the line is 20.
The second line passes through the point (0, -2) and (-2, -5). Hence:
[tex]y-y_1=\frac{y_1-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-2)=\frac{-5-(-2)}{-2-0} (x - 0)\\\\y=1.5x-2[/tex]
The equation of the line is y = 1.5x + 1 and y = 1.5x - 2
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Exponential Functions
In the exponential function y = 3 × q⁵ the starting value is 3.
What is an exponential function?
The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The given exponential function is -
y = 3 × q⁵
The exponential function is written in the form abˣ.
Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.
So, the initial or starting value in function y = 3 × q⁵ is -
a = 3
Therefore, the starting value is 3.
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find the solution to the initial value problem. dy dt = 8 y t , y(1) = 5
The solution to the initial value problem is y(t) = 5e^8t.
y(t) = 5e^8t
This is a separable differential equation. Separating the variables, we have
dy/dt = 8y
dy = 8y dt
Integrating both sides, we have
∫dy = ∫8ydt
y = 4e^8t + C
To find C, we use the initial condition, y(1) = 5
5 = 4e^8(1) + C
C = 5e^-8
Substituting C into the equation, we have
y(t) = 5e^8t
The solution to the initial value problem is y(t) = 5e^8t.
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